The bar graph below shows the highest score of different teams when they play for different cups. These are the four cups played by 4 teams in a year. Each team plays only one game against each team in each level. The team that won least number of matches is knocked out. The scores given in the graph are highest scores scored in any of the matches playing for that respective cup in a stipulated 50 overs cricket match.
Question: 1
If the given highest scores is taken, what is the least % share of Australia in the total scores of each Cup?
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Add each Cup's four scores, then find Australia's share of that total for every Cup.
Step 1: Find the total score of each Cup. Add the four team scores for every cup using the graph values. Cup A total = 324 + 309 + 315 + 280 = 1228. Cup B total = 285 + 300 + 310 + 320 = 1215. Cup C total = 260 + 275 + 255 + 300 = 1090. Cup D total = 290 + 330 + 310 + 315 = 1245.
Step 2: Find Australia's percentage share in each Cup. Divide Australia's score by that Cup's total and multiply by 100. Cup A: \( \frac{309}{1228} \times 100 = 25.16\% \). Cup B: \( \frac{300}{1215} \times 100 = 24.69\% \). Cup C: \( \frac{275}{1090} \times 100 = 25.23\% \). Cup D: \( \frac{330}{1245} \times 100 = 26.51\% \).
Step 3: Compare the four shares and pick the smallest. The shares are 25.16%, 24.69%, 25.23% and 26.51%. The smallest value is Cup B at about 24.7%.
Final Answer: Australia's least percentage share across the four cups is about 24.7%, from Cup B. \[ \boxed{24.7\%} \]
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Question: 2
In which Cup the % of increase in highest score of Sri Lanka is high when compared to the highest score in previous Cup?
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Compare each Cup's Sri Lanka score with the Cup right before it, and ignore any drop.
Step 1: List Sri Lanka's highest score in each Cup. From the graph, Sri Lanka scored 280 in Cup A, 320 in Cup B, 300 in Cup C and 315 in Cup D.
Step 2: Find the percentage change from each Cup to the next. Cup B compared to Cup A: \( \frac{320-280}{280} \times 100 = 14.29\% \) increase. Cup C compared to Cup B: \( \frac{300-320}{320} \times 100 = -6.25\% \), which is a decrease, not an increase. Cup D compared to Cup C: \( \frac{315-300}{300} \times 100 = 5\% \) increase.
Step 3: Compare the increases and reject any decrease. Only Cup B (14.29%) and Cup D (5%) show a genuine increase over the previous Cup. Cup B gives the higher increase of the two.
Final Answer: The highest percentage increase in Sri Lanka's score over the previous Cup happens in Cup B. \[ \boxed{\text{Cup B}} \]
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Question: 3
After the completion of tournament for cup A each team is given a rank based on their highest scores. If the highest score of India is same as the highest score of South Africa playing for cup C, what is the rank of team India playing for cup A?
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Swap India's Cup A score for South Africa's Cup C score, then rank the four Cup A scores.
Step 1: Note the real Cup A scores. Cup A scores are India 324, Australia 309, South Africa 315 and Sri Lanka 280.
Step 2: Apply the given condition. The question replaces India's Cup A score with South Africa's Cup C score, which is 255. So the working Cup A scores become Australia 309, South Africa 315, Sri Lanka 280 and India 255.
Step 3: Rank the four teams by score, highest first. South Africa 315 takes rank 1. Australia 309 takes rank 2. Sri Lanka 280 takes rank 3. India 255 takes rank 4.
Final Answer: With India's score replaced by 255, India finishes last in Cup A, at rank 4. \[ \boxed{4} \]
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Question: 4
If the highest scores of all teams in each cup is taken, what is the ratio of total runs scored by Sri Lanka and India in all the cups?
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Add each team's four cup scores separately, then write the two totals as a ratio.
Step 4: Write the ratio of the two totals. Sri Lanka to India is \( 1215 : 1159 \). Checking for a common factor shows 1215 and 1159 share no simple factor, so the ratio stays as is.
Final Answer: The ratio of Sri Lanka's total runs to India's total runs across all four cups is 1215 to 1159. \[ \boxed{1215 : 1159} \]
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Question: 5
If the runs scored by Australia and South Africa for cup B are of a final match, what is the required run rate of Australia to win the match playing all the stipulated overs?
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Find the target Australia must chase and divide it by the 50 overs.
Step 1: Note the Cup B scores of the two teams in the final. Australia scored 300 and South Africa scored 310 in Cup B.
Step 2: Decide who sets the target. South Africa's 310 is the higher score, so South Africa batted first and set the target. Australia must chase this target and score more runs to win the match.
Step 3: Find the target Australia needs. To win, Australia needs one run more than South Africa's total. Target = \( 310 + 1 = 311 \) runs.
Step 4: Find the required run rate over the full 50 overs. Required run rate = \( \frac{311}{50} = 6.22 \).
Final Answer: Australia needs a run rate of 6.22 runs per over across all 50 overs to win the match. \[ \boxed{6.22} \]
